Dylan Sabulsky
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 Jan 1 awarded Yearling Jul 2 awarded Curious May 13 awarded Yearling May 29 comment Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities Argue that (ijk) -> (xyz) and that the same answer holds for (jki) -> (yzx) etc. Changing the indices doesn't change the solution, for any permutation. You could write it out, explaining, or you could actually show the permutations are the same simply. May 26 answered Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities May 21 accepted Inelastic Scattering and coherent scatterng May 13 awarded Yearling Apr 13 awarded Fanatic Feb 21 comment Supplements for Kittel's Solid State Physics? Condensed Matter Physics by Marder may also interest you, but I think his section on crystallography is tiny. Feb 21 answered Supplements for Kittel's Solid State Physics? Feb 17 comment Rewriting Creation and Annihilation Operators Thanks so much for your help KDN. Awesome Feb 17 accepted Rewriting Creation and Annihilation Operators Feb 17 comment Rewriting Creation and Annihilation Operators of course, it is 1. $$[a,a^{\dagger}]=1$$ Feb 17 comment Rewriting Creation and Annihilation Operators I'm afraid it doesn't. Feb 17 comment Rewriting Creation and Annihilation Operators Great call, hadn't even considered it in my foolishness. $$[p_{i},r_{j}]=[p_{i},r_{j}]=-i\hbar \delta_{ij}$$ $$[R_{i},\pi_{j}]=0$$ $$[\pi_{i},\pi_{j}]=-i \epsilon_{ij} m \hbar \omega_{c}=-i \epsilon_{ij} \frac{\hbar^{2}}{l_{b}^{2}}$$ $$[R_{i},R_{j}]=i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},\rho_{j}]=-i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},\pi_{j}]=i \hbar \delta_{ij}$$ $$[p_{i},\pi_{j}]=-i \hbar \frac{e}{c} \frac{\partial A_{j}}{\partial r_{i}}$$ $$[R_{i},r_{j}]=i \epsilon_{ij} l_{b}^{2}$$ $$[\rho_{i},r_{j}]=-i \epsilon_{ij} l_{b}^{2}$$ Feb 17 comment Rewriting Creation and Annihilation Operators For context, I am studying the quantum Hall Effect, integer and fractional, and this came up in my instructors online notes. I am unsure why you would rewrite this, and further what is the best way to approach it. To expand on my idea, I was thinking to expand $\pi$ to $\vec{\pi}=m\vec{v}=\vec{p}-\frac{q}{c}\vec{A}$ and perhaps try from there. Feb 17 asked Rewriting Creation and Annihilation Operators Feb 12 answered Projectile motion, canon vs cliff Feb 12 comment Projectile motion, canon vs cliff Working on this now. Also, the velocity of the ball at the top of the cliff is zero because if it were not, it would go higher than 85m; the question tells you it just reaches the top. Feb 12 answered How can I understand work conceptually?